Question:
a farmer wishes to grow a 100 m sq rectangular vegetable garden. since he has with him the only 30m barbed wire, he fences three sides of the rectangular garden letting the compound wall of his house act as fourth side fence.find the dimensions of his garden
Answer:
Let l is the length and b is the breadth of the rectangular vegetable garden.
Now, area of the rectangle = l * b
=> 100 = l * b
=> b = 100/l
Again given, the sum of the three sides of the rectangular garden = 30
=> 2b + l = 30
=> 2 * (100/l) + l = 30
=> 200/l + l = 30
=> 200 + l2 = 30l
=> l2 - 30l + 200 = 0
=> (l - 20)*(l - 10) = 0
=> l = 10, 20
Now, when l = 10, b = 100/10 = 10
When l = 20, b = 100/20 = 5
Now, l = b = 10 is not possible because the garden is rectangular.
So, l = 20, and b = 5
Hense, 20 cm is the length and 5 cm is the breadth of the vegetable garden.
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